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%I M3354 #50 Sep 08 2022 08:44:32
%S 1,4,9,16,25,35,46,58,71,85,100,116,133,151,170,190,211,233,256,280,
%T 305,331,358,386,415,445,476,508,541,575,610,646,683,721,760,800,841,
%U 883,926,970,1015,1061,1108,1156,1205
%N Expansion of (1 + x - x^5) / (1 - x)^3.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A004120/b004120.txt">Table of n, a(n) for n = 0..10000</a>
%H D. R. Breach, <a href="http://www.jstor.org/stable/2029239">Solution to Problem 68-16</a>, SIAM Rev. 12 (1970), 294-297.
%H D. R. Breach, <a href="/A004120/a004120.pdf">Letter to N. J. A. Sloane, Jun 1980</a>
%H Philippe Flajolet, <a href="http://algo.inria.fr/libraries/autocomb/balls-html/balls1.html">Balls and urns, etc.</a> A problem in submarine detection (solution to 68-16)
%H M. Klamkin, ed., <a href="http://dx.doi.org/10.1137/1.9781611971729">Problems in Applied Mathematics: Selections from SIAM Review</a>, SIAM, 1990; see pp. 109-111.
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1)
%F a(n) = n*(n + 11)/2 - 5, n>=3. - _R. J. Mathar_, Mar 15 2011
%p (1+x-x^5)/(1-x)^3;
%p A004120:=(-1-z+z**5)/(z-1)**3; # _Simon Plouffe_ in his 1992 dissertation
%t i=7;s=1;lst={s};Do[s+=n+i;If[s>=0, AppendTo[lst, s]], {n, 0, 6!, 1}];lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 30 2008 *)
%t CoefficientList[Series[(1+x-x^5)/(1-x)^3,{x,0,50}],x] (* or *) Join[ {1,4,9}, LinearRecurrence[{3,-3,1},{16,25,35},50]] (* _Harvey P. Dale_, Oct 11 2011 *)
%o (Magma) [1,4,9],[n*(n+11)/2-5: n in [3..30]]; // _Vincenzo Librandi_, Oct 08 2011
%o (PARI) a(n)=if(n>2,(n^2+11*n)/2-5,(n+1)^2) \\ _Charles R Greathouse IV_, Sep 30 2015
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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